Question

reflections find the coordinates
the point e(-3,2) is reflected over the y-axis. what are the coordinates of the resulting point e?
image of coordinate plane with point e and y-axis
options: e(3,2); e(-3,-2); e(-3,2); e(3,-2)

Explanation:

Step1: Recall reflection over y - axis rule

When a point \((x,y)\) is reflected over the \(y\) - axis, the rule is that the \(x\) - coordinate changes its sign and the \(y\) - coordinate remains the same. Mathematically, if we have a point \(P(x,y)\), after reflection over the \(y\) - axis, the new point \(P'\) has coordinates \((-x,y)\).

Step2: Apply the rule to point \(E(-3,2)\)

For the point \(E(-3,2)\), here \(x=-3\) and \(y = 2\). Using the reflection over \(y\) - axis rule \((x,y)\to(-x,y)\), we substitute \(x=-3\) into \(-x\). So, \(-x=-(-3)=3\) and \(y\) remains \(2\). So the coordinates of \(E'\) are \((3,2)\).

Answer:

\(E'(3,2)\)